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Bellman Systems with Mean Field Dependent Dynamics |
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Citation: |
Alain BENSOUSSAN,Miroslav BUL'{I}v{C}EK,Jens FREHSE.Bellman Systems with Mean Field Dependent Dynamics[J].Chinese Annals of Mathematics B,2018,39(3):461~486 |
Page view: 1072
Net amount: 1590 |
Authors: |
Alain BENSOUSSAN; Miroslav BUL'{I}v{C}EK;Jens FREHSE |
Foundation: |
This work was supported by the National Science
Foundation (Nos.DMS 1303775, DMS 1612880), the Hong Kong SAR
Research Grant Council (Nos.GRF 500113, 11303316), Hausdorff
Center for Mathematics at University of Bonn and the Czech Science
Foundation (No.16-03230S). |
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Abstract: |
The authors deal with nonlinear elliptic and parabolic systems that
are the Bellman like systems associated to stochastic differential
games with mean field dependent dynamics. The key novelty of the
paper is that they allow heavily mean field dependent dynamics. This
in particular leads to a system of PDE's with critical growth, for
which it is rare to have an existence and/or regularity result. In
the paper, they introduce a structural assumptions that cover many
cases in stochastic differential games with mean field dependent
dynamics for which they are able to establish the existence of a
weak solution. In addition, the authors present here a completely
new method for obtaining the maximum/minimum principles for systems
with critical growths, which is a starting point for further
existence and also qualitative analysis. |
Keywords: |
Stochastic games, Bellman equation, Mean field equation, Nonlinearelliptic equations, Weak solution, Maximum principle |
Classification: |
35J60, 35K55, 35J55, 35B65 |
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